In the case of Savile, there were five reported offences, from 1979 to 1988, which ranged from sexual assault to rape. Photograph: PA

Police have apologised to victims of Jimmy Savile and one of his friends after concluding that officers missed opportunities to properly investigate the two men over alleged child abuse when they were still alive.

North Yorkshire police made the apology after an investigation into the activities of Savile and the former mayor of Scarborough, Peter Jaconelli, concluded there would have been enough evidence to consider prosecuting them.

The force said 35 people had come forward with allegations about the pair.

A spokesman said 32 cases related to Jaconelli, between 1958 and 1998, included allegations of indecent assault, inciting a child to engage in sexual activity, gross indecency and rape. In the case of Savile, there were five reported offences, from 1979 to 1988, which ranged from sexual assault to rape. Two people claimed to be victims of both men.

The spokesman said: “Sufficient evidence has been uncovered to suggest that, had they been alive today, files would have been submitted for consideration by the Crown Prosecution Service regarding potential criminal charges against Peter Jaconelli and Jimmy Savile, relating to young people.

“However, it should be noted that it has not been possible to pursue those lines of inquiry which would have involved interviews with the individuals concerned, during which they may have disputed the allegations against them.”

North Yorkshire police launched Operation Hibiscus in February after a BBC Inside Out programme prompted 35 people to come forward with reports of sexual abuse by Jaconelli and Savile.

Assistant chief constable Paul Kennedy said: “The findings of Operation Hibiscus clearly suggest that there would have been sufficient evidence from 35 individual victims for the Crown Prosecution Service to consider criminal charges against Peter Jaconelli and Jimmy Savile, had they been alive today.

“The available information indicates that, historically, the police missed opportunities to look into allegations against these men whilst they were still alive.

“Today, North Yorkshire police apologises to the victims who made the brave decision to come forward during the past 18 months.”

Kennedy said: “It is important that the victims have been able to make their allegations heard, and that their cases have been comprehensively examined by the police, regardless of the passage of time.

“It is a matter of great regret that, from the outset of the investigation, there was no prospect of true justice being achieved as the suspects are deceased.

“However, I hope the victims have gained a measure of closure from knowing that matters have now been investigated as fully as possible by North Yorkshire police.

“It is never too late to report information to the police and seek help and support. Nobody should suffer in silence.”

He said the investigation team has contacted the victims to explain the findings of the inquiry, and to ensure they have continuing access to all available support as victims of sexual abuse.

In April, North Yorkshire police voluntarily referred itself to the Independent Police Complaints Commission (IPCC) in relation to the Savile/Jaconelli allegations.

It subsequently referred other related matters to the IPCC.

The commission has already announced that one serving detective sergeant has been served with a misconduct notice to advise him his conduct is subject to IPCC investigation.

The officer has been interviewed by an IPCC investigator and the inquiry is continuing.

The commission referred matters relating to whether records on Savile and his associates were properly disclosed to Her Majesty’s Inspectorate of Constabulary (HMIC) and IPCC back to North Yorkshire police for consideration.

In relation to this, Kennedy said: “A comprehensive investigation into these matters has now been completed by the Professional Standards Department.

“It concluded that there was no evidence of misconduct but there was evidence of organisational failure, with a number of lessons to be learned which have now been rectified for the future.”

He said: “Whilst there were failings to report some relevant information to the HMIC and IPCC, there is no evidence to suggest North Yorkshire police failed in its responsibility to support Operation Yewtree, the national investigation concerning Savile.”

Kennedy said his Professional Standards Department was continuing to investigate further issues relating to the Jaconelli and Savile investigation in Scarborough during the 1980s.

Savile was a frequent visitor to Scarborough throughout his life and had a sea-view flat in the resort. Jaconelli was a well-known local businessman.

Jessica Standley, of Slater & Gordon, which represents 169 victims, said: “The victims will take some comfort from the apology.

“Savile’s victims were routinely ignored when they reported the abuse and countless opportunities to investigate him were missed, not just by police but also in other organisations he was involved with.

“Hopefully, we are learning the lessons of the past and no one will ever get away with the systematic reign of abuse Savile did. Changing the law so the reporting of child abuse was mandatory within regulated institutions – which has already been backed by the Liberal Democrats and Labour – would further protect our children in the future and I would urge the government to bring new legislation.”